The 49-year-old actor and the French actress, 39, have a 13-year-old daughter, Lily-Rose, and a 9-year-old son, Jack. The family has lived in France, where Depp also avoided the Hollywood spotlight.

Depp, who most recently appeared in Tim Burton's Dark Shadows, received the Generation Award at the MTV Movie Awards earlier this month, bypassing an acceptance speech to perform songs onstage with the Black Keys.